Write the following series in sigma notation.
9, plus, 19, plus, 29, plus, 39, plus, 49
9+19+29+39+49

The given series \(9 + 19 + 29 + 39 + 49\) follows an arithmetic progression with the first term \(a_1 = 9\) and the common difference \(d = 10\). To express this in sigma notation, let's identify the general term for the series.

The general term of an arithmetic series is given by:
\[
a_n = a_1 + (n-1) \cdot d
\]
Substituting \(a_1 = 9\) and \(d = 10\), the general term becomes:
\[
a_n = 9 + (n-1) \cdot 10 = 10n - 1
\]
Now, we can express the sum in sigma notation for \(n\) from 1 to 5, since there are 5 terms in the series:

\[
\sum_{n=1}^{5} (10n - 1)
\]

This is the sigma notation for the given series.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the sum of an arithmetic series?
2. Can you express a geometric series in sigma notation?
3. How is the common difference calculated in an arithmetic progression?
4. What happens if the common difference in an arithmetic series is negative?
5. How can sigma notation be applied to represent infinite series?

**Tip:** Always verify the first few terms by plugging values of \(n\) into the general term formula to check your sigma notation.

Write the following series in sigma notation. 9 + 19 + 29 + 39 + 49

Learn how to express the arithmetic series 9 + 19 + 29 + 39 + 49 in sigma notation. This step-by-step solution demonstrates how to find the general term of the series and apply sigma notation. Suitable for students in Grades 9-10.

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